Here we provide a unified theoretical description of two different physical situations in which liquid jets are expelled out of the bulk of a liquid as a consequence of the capillary collapse of a void. We demonstrate that the velocity field giving rise to the emergence of these jets can be calculated as the flow generated by a line of sinks with a length and an intensity that can be expressed in terms of the initial cavity radius and the wavelength and velocity of the capillary waves propagating along the cavity walls. The predicted jet speeds, which are expressed through algebraic equations, are in good quantitative agreement with those obtained from experiments and from the simulations of bubbles bursting on a free surface or after the implosion of the crater formed when a drop impacts a liquid pool.

Oscillatory flow features are common in the unstart of hypersonic mixed-compression intakes and can be classified as low-amplitude or high-amplitude oscillatory unstarted flows. The low-amplitude oscillatory unstarted flow is driven by the shear layer from shock interactions ahead of the cowl, while the high-amplitude oscillatory unstarted flow is driven by the separation caused by shock–boundary-layer interaction on the ramp. While previous studies have observed these flow features and reported their associated frequency, there is no simple criterion available for predicting which mode will occur, and there is a lack of consensus on the appropriate frequency scaling parameter. We study a mixed-compression hypersonic intake in a hypersonic wind tunnel by varying the internal contraction ratio and the throttling ratio to observe various kinds of unstart regimes. Two significant conclusions emerge from considering the results for high-throttling-ratio conditions $(TR > 0.55)$ from the current as well as previous studies. Firstly, the actual shock-on-lip condition at the cowl corresponding to the unthrottled condition, as observed from schlieren images, demarcates the boundary between the two modes of oscillatory unstart flows upon throttling. Secondly, a suitable length scale $(l^*)$, defined as the extent of the subsonic region in the unstarted flow (as observed from the experimental schlieren images), gives the appropriate frequency scaling parameter ($f^* = a_0/4l^*$ where $a_0$ is the stagnation acoustic speed).

The paper addresses the fluid–structure interaction of submerged aquatic canopies, with particular focus on the complex interplay between coherent flow structures and the motion of vegetation elements. New insights into the underlying mechanisms are gained from a large eddy simulation of a submerged model canopy flow. The model canopy is made up of 800 highly flexible blades, each individually resolved by an immersed boundary method. The obtained high-resolution flow data reveal well-known coherent turbulent structures, including velocity streaks, Kelvin–Helmholtz (KH) vortices in the mixing layer as well as hairpin (HP) vortices in the outer flow region. The present results show that the interaction of these prototypical structures plays a key role creating unique turbulent features such as composite KH/HP vortices located between a high-speed and low-speed streak. Under the influence of these pronounced eddies, groups of blades respond by a strong local reconfiguration. Due to the convection of the coherent structures by the mean flow this causes an apparent wave-like motion of the canopy in streamwise direction, known as monami. A frequency analysis of this phenomenon shows that the vegetation responds almost passively, merely reflecting local flow conditions.

The paper reports on three direct numerical simulations of sediment transport with different prototypical non-spherical particle shapes, ranging from prolate to oblate to a triaxial ellipsoidal shape, and a fourth simulation with spherical particles. All physical and numerical parameters of these simulations are identical, including bulk Reynolds number, equivalent particle diameter and sphericity of the non-spherical particles, so that the shape is the only difference. Numerous statistical quantities assessing the computed solutions are presented, such as mean particle velocity, sediment-bed porosity, equivalent roughness height, mean fluid velocity and Reynolds stresses. These allow a detailed analysis and reveal the considerable influence of the particle shape on the entire flow: fluid as well as particles. It is found that oblate spheroids yield the highest porosity among the four cases and spherical particles the lowest mean porosity. Prolate particles exhibit the strongest tendency to form spanwise clusters and generate the highest total bed friction. Triaxial ellipsoids representing natural medium-size sand particles yield results in between these cases, still exhibiting substantial differences with respect to spherical particles. The mean sediment transport rate is determined in all four cases showing that this quantity cannot be correlated to the mean shear stress of the fluid alone. This emphasises the importance of the particle shape in modelling the transport of natural sediment, and the results provide well-controlled data points for this task.

The motion of glaciers over their bedrock or drops of fluid along a solid surface can vary dramatically when these substrates are lubricated. We investigate the coupled flow of a gravity current (GC) of a strain-rate softening fluid that is lubricated by a denser, lower-viscosity Newtonian fluid. We present a set of experiments in which such GCs are discharged axisymmetrically and at constant flux over a flat surface. Using imaging techniques, we follow the evolution of the front and thickness field of each fluid. We find that, unlike purely Newtonian lubricated GCs, the fronts of the non-Newtonian and lubricating Newtonian fluids have a power-law time evolution with different exponents. Each of these exponents is similar to that of a non-lubricated GC of the same fluid. Nevertheless, the fronts of our lubricated GCs evolve faster than those of the corresponding non-lubricated GCs owing to larger intercepts. In addition, in contrast with the monotonically declining thickness of non-lubricated GCs, the thickness of the lubricated, non-Newtonian fluid is nearly uniform, and that of the lubricating fluid is non-monotonic with localised spikes. Despite these complex thickness patterns, lubricated GCs remain axisymmetric as long as the flux of the lubricating fluid is sufficiently smaller than that of the non-Newtonian fluid.

A rigorous bound on the energy dissipation in the flow around a sphere is derived analytically. The bound is allowed to depend on the viscosity of the fluid, the radius of the sphere, the free-stream velocity and the amplitude of the difference between the actual flow field and the irrotational flow around the sphere. The bound becomes asymptotically independent of viscosity as the Reynolds number tends to infinity. Provided that the velocity fluctuations are of the same order as the free-stream velocity, the scaling of the bound is consistent with a Reynolds-number-independent drag coefficient at high Reynolds numbers.

We investigate the removal of a dense bottom layer by a gravity current, via Navier–Stokes simulations in the Boussinesq limit. The problem is governed by a dimensionless thickness parameter for the bottom layer, and by the ratio of the density differences between bottom layer, gravity current and ambient fluids. A quasisteady gravity current forms that propagates along the interface and displaces some of the dense bottom fluid, which accumulates ahead of the gravity current and forms an undular bore or a series of internal gravity waves. Depending on the ratio of the gravity current front velocity to the linear shallow-water wave velocity, we observe the existence of different regimes, characterized by small-amplitude waves or by a train of steep, nonlinear internal waves. We develop a semiempirical model that provides reasonable estimates of several important flow properties. We also formulate a more sophisticated, self-contained model based on the conservation principles for mass and vorticity that does not require empirical closure assumptions. This model is able to predict such quantities as the gravity current height and the internal wave or bore velocity as a function of the governing dimensionless parameters, generally to within approximately a 10 $\%$ accuracy. An energy budget analysis provides information on the rates at which potential energy is converted into kinetic energy and then dissipated, and on the processes by which energy is transferred from the gravity current fluid to the dense and ambient fluids. We observe that the energy content of thicker and denser bottom layers grows more rapidly.

We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^{7}$, convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry – periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary, thereby controlling its morphology characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.

We conduct a theoretical study of a two-phase fluid–structure interaction problem in which air is driven at constant volume flux into a liquid-filled Hele-Shaw channel whose upper boundary is an elastic sheet. A depth-averaged model in the frame of reference of the advancing air–liquid interface is used to investigate the steady and unsteady interface propagation modes via numerical simulation. In slightly collapsed channels, the steadily propagating interface adopts a shape that is similar to the classic Saffman–Taylor finger in rigid Hele-Shaw cells. As the level of initial collapse increases, the induced gradients in channel depth alter the morphology of the propagating finger and promote a variety of instabilities from tip splitting to small-scale fingering on the curved interface, in qualitative agreement with experiments. The model has a complex solution structure with a wide range of stable and unstable, steady and time-periodic modes, many of which have similar driving pressures. We find good quantitative agreement between our model and the experimental data of Ducloué et al. (J. Fluid Mech., vol. 819, 2017, p. 121) for the finger width, sheet profile and finger pressure, provided that corrections to account for the presence of liquid films on the upper and lower walls of the channel are included in the model.

We study the steady force acting on a rigid spherical particle immersed in an ideal gas and impinged by a standing acoustic wave. The acoustic wavelength and particle radius are assumed much larger and smaller, respectively, than the molecular mean-free path. To analyse the system, an asymptotic scheme is constructed, combining an inviscid continuum description in the far field with a free-molecular formulation for the near gas–surface interaction. The computation yields a closed-form expression for the steady acoustic force. The free-molecular solution is compared with a formerly derived result in the continuum regime (Doinkov, Proc. R. Soc. Lond. A, vol. 447, 1994, pp. 447–466), and the latter is found characteristically larger by an order of magnitude at a given ratio between the particle radius and the acoustic wavelength. Markedly, the size of the acoustic force at ballistic flow conditions may become up to four orders of magnitude larger than the typical gravitational force, suggesting the feasibility of nano-particle acoustic levitation.

In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with geostrophically balanced turbulent flows. Advection and refraction by such flows lead to wave scattering, redistributing IGW energy in the position–wavenumber phase space. We give a detailed description of this process by deriving a kinetic equation governing the evolution of the IGW phase-space energy density. The derivation relies on the smallness of the Rossby number characterising the geostrophic flow, which is treated as a random field with known statistics, makes no assumption of spatial scale separation, and neglects wave–wave interactions. It extends previous work restricted to near-inertial waves, barotropic flows or waves much shorter than the flow scales. The kinetic equation describes energy transfers that are restricted to IGWs with the same frequency, as a result of the time scale separation between waves and flow. We formulate the kinetic equation on the constant-frequency surface – a double cone in wavenumber space – using polar spherical coordinates, and we examine the form of the two scattering cross-sections involved, which quantify energy transfers between IGWs with, respectively, the same and opposite directions of vertical propagation. The kinetic equation captures both the horizontal isotropisation and the cascade of energy across scales that result from scattering. We focus our attention on the latter to assess the predictions of the kinetic equation against direct simulations of the three-dimensional Boussinesq equations, finding good agreement.

In this work, we investigate the dynamics of long non-axisymmetric fibres in turbulent channel flow. The experimental facility is the TU Wien Turbulent Water Channel, consisting of a closed water channel (aspect ratio of 10), and the experiments are performed at a shear Reynolds number of 360. Fibres are neutrally buoyant rods that are curved and characterised by a length-to-diameter ratio of 120. Illumination is provided by a laser sheet and the motion of fibres is recorded by four high-speed cameras in a fully developed flow section. We apply multiplicative algebraic reconstruction techniques to the recorded images from four high-speed cameras to identify the three-dimensional location, shape and orientation of the fibres. The fibres are also tracked in time to obtain their three-dimensional vectors of velocity and rotation rate. We investigate the behaviour of the fibres, from the near-wall region to the channel centre, and we produce original statistics on the effect of curvature of the fibres on their orientation and rotation rate. Specifically, we measured the orientation and rotation rate of the fibres, and we can confirm that in the centre, the most homogeneous part of the channel, statistics, although influenced by the curvature, bear similarities to those obtained in previous investigations in homogeneous isotropic turbulence. In addition, we have been able to compare the tumbling rate of our long non-axisymmetric fibres with previous solutions for curved ellipsoids in simple shear flow.

An experimental investigation was carried out in a low-turbulence wind tunnel to study the early development of artificially initiated turbulent spots in a laminar boundary layer over a flat plate. The reproducibility of the experiments allowed us to observe fine structural details that have not been observed previously. Initial velocity disturbances quickly developed into hairpin-like structures that multiplied downstream, which increased the width, length and height of the incipient turbulent spots. Only those disturbances that were greater than a threshold value developed into turbulent spots while the others decayed. The rate of development was also affected by the duration of the initial disturbances. We found that the behaviour of turbulence generation within a turbulent spot is similar to the burst events in the turbulent boundary layer, where ejection events are followed by sweep events.

Studying the effect of different in-stream fluvial turbines siting on river morphodynamics allowed us to witness the onset of a time-averaged, large-scale, alternate distortion of bed elevations, which could not be exclusively related to the turbine rotor blockage. The longitudinal profiles of this two-dimensional bathymetric perturbation resemble those of steady fluvial bars. In this contribution we generalize the problem addressing a spatially impulsive, asymmetric distribution of drag force in the channel cross-section. This is experimentally investigated through the deployment of differently sized grids perpendicular to the flow, and analytically explored as a finite perturbation of an open channel flow over an erodible sediment layer, as described by a coupled flow–sediment shallow water equation. The steady solutions of this fluvial morphodynamic problem, physically represented by alternate bars scaling with the channel width, highlight the importance of the resonant conditions in defining the spatial extent of the bed deformation. The equations further suggest that in very shallow flows any asymmetric obstruction may lead to an upstream propagation of the steady bars, consistent with previous studies on the effects of channel curvature. In broad terms, this study provides the preliminary framework to control the onset of river meandering through imposed finite perturbations of the cross-section. In a more applied sense, it provides a tool to predict non-local scour–deposition patterns associated with the deployment of energy converters or other flow obstructions.

Liquid-infused surfaces (LISs) are a promising technique for reducing friction, fouling and icing in both laminar and turbulent flows. Previous work has demonstrated that these surfaces are susceptible to shear-driven drainage. Here, we report a different failure mode using direct numerical simulations of a turbulent channel flow with liquid-infused longitudinal grooves. When the liquid–liquid surface tension is small and/or grooves are wide, we observe travelling-wave perturbations on the interface with amplitudes larger than the viscous sublayer of the turbulent flow. These capillary waves induce a roughness effect that increases drag. The generation mechanism of these waves is explained using the theory developed by Miles for gravity waves. Energy is transferred from the turbulent flow to the LIS provided that there is a negative curvature of the mean flow at the critical layer. Given the groove width, the Weber number and an estimate of the friction Reynolds number, we provide relations to determine whether a LIS behaves as a smooth or rough surface in a turbulent flow.

We derive equations of motion that describe the dynamics of a fluid confined within an elastic nanotube subject to periodic bending deflections. We use the principle of least action applied to a continuous open system at constant temperature. We solve the equations analytically in two limiting situations: when the tube oscillations are so small that they do not affect the fluid motion, but this one affects the tube dynamics; and when the flow magnitude is so small that it has no influence on the tube dynamics, but this one affects fluid motion. In the first case, we find out that the characteristic bending frequency spectrum of the tube depends not only on the magnitude of flow velocity, as previously stated in the literature, but also on the fluid velocity profile. This could constitute the basis of a strategy for indirect determination of the slip length in carbon nanotubes conveying flow via measurement of the buckling speed. In the second case, we find that tube vibrations can modify the dynamics of the fluid. Particularly, for a fluid subject to a constant pressure gradient, the tube motion induces an oscillatory motion in the fluid with twice the frequency of the tube. Moreover, the amplitude of the oscillatory fluid motion persists at high frequencies. This could constitute a strategy to generate high-frequency flows at nanoscales. Our results open up a panorama to control flow across nanotubes via tube vibrations, which could be complementary to chemical functionalization of nanostructures.

The well-known thermal capillary wave theory, which describes the capillary spectrum of the free surface of a liquid film, does not reveal the transient dynamics of surface waves, e.g. the process through which a smooth surface becomes rough. Here, a Langevin model is proposed that can capture this dynamics, goes beyond the long-wave paradigm which can be inaccurate at the nanoscale, and is validated using molecular dynamics simulations for nanoscale films on both planar and cylindrical substrates. We show that a scaling relation exists for surface roughening of a planar film and the scaling exponents belong to a specific universality class. The capillary spectra of planar films are found to advance towards a static spectrum, with the roughness of the surface $W$ increasing as a power law of time $W\sim t^{1/8}$ before saturation. However, the spectra of an annular film (with outer radius $h_0$) are unbounded for dimensionless wavenumber $qh_0<1$ due to the Rayleigh–Plateau instability.

Cylinder stubs of finite length, mounted in a wall-normal manner on a flat plate, exert considerable control on their wake when rotating around their central axis. The present paper investigates these effects with linear stability theory and a direct numerical simulation. Three configurations are considered: evenly spaced corotating roughness elements, as well as positive and negative counter-rotating roughness pairs. Here, ‘positive’ and ‘negative’ are defined in accordance with the induced high- and low-speed streaks, respectively. A primary feature of the rotating-cylinder-induced wake is a ‘dominating inner vortex’ (DIV), which intensifies the lift-up effect and creates high-amplitude streaks. Linear stability analysis shows that the modified streaky flow is capable of effectively stabilizing Tollmien–Schlichting (TS) modes. The mechanism of TS mode stabilization, as found by a perturbation kinetic energy analysis, is attributed to the reduction of the wall-normal perturbation production. On the other hand, an inviscid inflectional instability mode related to the presence of the roughness appears which destabilizes the boundary-layer flow, primarily due to an increase in wall-normal perturbation energy production, but also due to increasing spanwise energy production, depending on the case. The inflectional instability roughness mode is more amplified with thicker cylinders since the induced DIV tends to support longer-living inflection points. Regarding an imaginable laminar–turbulent transition delay, positive rotating thinner roughness pairs would be preferable.

Instability and transition in the boundary layer on a slender cone ($60^{\circ }$ apex angle) rotating in still fluid are investigated using hot-wire anemometry as well as through linear stability analysis. In contrast to broad cones (including the disk), where a cross-flow instability dominates the transition and different studies report similar transition Reynolds numbers, the reported transition Reynolds numbers on slender cones are scattered. The present experiments provide quantitative experimental datasets and the stability and transition are evaluated based on both the Reynolds number and a Görtler number. The results consistently show that the instability development depends on the Görtler number rather than the Reynolds number and that transition starts at a well-defined Görtler number, whereas the transition Reynolds number depends on the rotational rate. The measured disturbance that first grows in the laminar region has a frequency approximately the same as or twice the rotational rate of the cone, which according to the stability analysis corresponds to the critical frequency of a slightly inclined vortex structure with respect to the cone axis or an axisymmetric vortex structure. These structures are similar to those observed in the flow visualisations of Kobayashi & Izumi (J. Fluid Mech., vol. 127, 1983, pp. 353–364) and considered as being due to a centrifugal instability.

The instantaneous structure of a turbulent boundary layer that has developed beneath freestream turbulence (FST) was investigated with planar particle image velocimetry. Measurements were performed in the streamwise–wall-normal plane at a position $Re_x = U_\infty x / \nu = 2.3 \times 10^6$ downstream of the boundary layer origin. FST was generated with an active grid placed upstream of a boundary layer plate. Three cases were investigated with FST intensity increasing from approximately zero to 12.8 %. It is shown that internal interfaces, separating areas of approximately uniform momentum, are present for all cases and show a dependence on the FST. In particular, the number and length of the uniform-momentum zones (UMZs) decrease with increasing FST. The modal velocities associated with the UMZs are distributed in approximately the same way regardless of the condition of the outer flow, suggesting a degree of resilience of the instantaneous structure to the freestream. Tracking the top edge of the upper-most UMZ revealed that this contour approaches the wall for increasing FST. Finally, it is demonstrated that the observed first-order phenomena in a turbulent boundary layer subjected to FST can be modelled by superimposing an isotropic turbulence field on a turbulent boundary layer field, which supports the hypothesis that the underlying structure of the boundary layer appears to remain largely intact if the naturally occurring fluctuations in the turbulent boundary layer exceed the energy of the FST.